Method for drooping mesh vertices over rounded objects
Just from the looks of it, I'd say that the object you want to shrink has a way too low vertex count to fit the model. Try to add some loop cuts and then try the shrink wrap modifier again.

Depending on what you want the end result look like, it's also possible to copy a part of your mesh, convert that part into a new object (hit P) and go from there. 

There is also the possibility of using physics but I never tried it with solid objects.